Sqad, it does depend on the terms of the contract. But my view in all probability is "yes".
No win, no fee does not mean that you do not pay costs if you lose - it means you do not pay your own lawyers. You are generally still liable for costs on the basis that the loser normally pays. These type of arrangements are normally attractive to those who do not have any assets since enforcing an adverse costs order against someone with nothing will never succeed.
Very often to ensure that you do not pay costs on a loss when you engage a no win no fee firm, you also buy an insurance policy. This is not mandatory though. Check to see if you did actually take out such a policy.
The caveat to this though is I have absolutely no idea how Spanish law and Spanish lawyers operate, nor the Spanish civil code.